Anomalous Diffusion in the Nonasymptotic Regime

C.A. CONDAT; J. RANGEL; P.W. LAMBERTI

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

The American Physical Society

Año: 2002 vol. 65 p. 261381 - 261389

1063-651X

We analyze some properties of the one-dimensional Lévy flights, assuming that the one-step transition rates depend on the flight length x as pa(x) ~ x-(a+2). For flights on a finite, (2M+1)-site lattice, we can define an effective, size-dependent, diffusion coefficient Da(M) ~ [M1-a - 1]/(1-a) if a < 1, with D1(M) ~ ln(M). Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments <xR> are well defined provided that a > R-3. These Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments <xR> are well defined provided that a > R-3. These Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments <xR> are well defined provided that a > R-3. These Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments <xR> are well defined provided that a > R-3. These effective, size-dependent, diffusion coefficient Da(M) ~ [M1-a - 1]/(1-a) if a < 1, with D1(M) ~ ln(M). Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments <xR> are well defined provided that a > R-3. These Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments <xR> are well defined provided that a > R-3. These Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments <xR> are well defined provided that a > R-3. These Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments <xR> are well defined provided that a > R-3. These effective, size-dependent, diffusion coefficient Da(M) ~ [M1-a - 1]/(1-a) if a < 1, with D1(M) ~ ln(M). Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments <xR> are well defined provided that a > R-3. These Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments <xR> are well defined provided that a > R-3. These Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments <xR> are well defined provided that a > R-3. These Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments <xR> are well defined provided that a > R-3. These effective, size-dependent, diffusion coefficient Da(M) ~ [M1-a - 1]/(1-a) if a < 1, with D1(M) ~ ln(M). Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments <xR> are well defined provided that a > R-3. These Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments <xR> are well defined provided that a > R-3. These Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments <xR> are well defined provided that a > R-3. These Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments <xR> are well defined provided that a > R-3. These pa(x) ~ x-(a+2). For flights on a finite, (2M+1)-site lattice, we can define an effective, size-dependent, diffusion coefficient Da(M) ~ [M1-a - 1]/(1-a) if a < 1, with D1(M) ~ ln(M). Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments <xR> are well defined provided that a > R-3. These Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments <xR> are well defined provided that a > R-3. These Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments <xR> are well defined provided that a > R-3. These Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments <xR> are well defined provided that a > R-3. These if a < 1, with D1(M) ~ ln(M). Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments <xR> are well defined provided that a > R-3. These are well defined provided that a > R-3. These moments exhibit a power-law singularity if a ® 1- and R >.2/3. The short- and intermediate-time properties of the generalized mean-square displacement are then studied numerically. This work suggests the conditions under which the asymptotic analytical formulas (obtained in the literature by the use of the generalized central limit theorem) could be applied to finite-time experiments. These formulas should work much better if a is close to zero than in the a ® 1- neighborhood.